[Haskell-cafe] How to split this string.

[AUGER Cédric]

Le Wed, 04 Jan 2012 17:49:15 +0000,
Steve Horne <sh006d3592 at blueyonder.co.uk> a écrit :

> On 04/01/2012 16:47, Steve Horne wrote:
> >
> >   (a == a)
> >   reflexivity : (a == b) => (b == a)
> >   transitivity : (a == b) && (b == c) => (a == c)
> >
> Oops - that's...
> 
> reflexivity :  (a == a)
> symmetry : (a == b) => (b == a)
> transitivity : (a == b) && (b == c) => (a == c)
> 
> An equivalence relation is a relation that meets all these conditions.
> 
> 

I prefer to use "transymmetry" (although I guess it is not a regular
word):

reflexivity: a ≃ a
transymmetry: ∀ a b. b≃a ⇒ ∀ c. c≃a ⇒ b≃c

so I only have 2 rules.
transymmetry is trivially derived from transitivity and symmetry.
symmetry is trivially derived from reflexivity and transymmetry.
transitivity is trivially derived from symmetry and transymmetry
 (and thus from transymmetry and reflexivity)

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